Ordu University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
MAT30320121310	DIFFERENTIAL GEOMETRY I	Compulsory	3	5	6

Level of Course Unit

First Cycle

Objectives of the Course

To teach and adopt students the theory and applications of geometry.

Name of Lecturer(s)

Yrd. Doç. Dr. Süleyman ŞENYURT

Learning Outcomes

1	will understand the geometry of theory and practice.

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Differentiable transformations. Tangent space. Tangent and cotangent vector fields. 1-forms, k-forms. Tensors. Outer product of differential forms. Parametric representation of a curve in space, velocity vector, covariant derivative. Frenet vectors of a curve, Frenet planes, curves, geometrical interpretation of the curves, the circle of curvature, curvature sphere, the axis of curvature, osculator sphere. Spherical curves. Inclined curves. Involute and evolute. Bertrand curve pairs. Global indicators of a curve.

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Differentiable transformations
2	Tangent space
3	Tangent and cotangent vector fields
4	1-forms
5	k-forms
6	Tensors
7	Outer product of differential forms
8	Midterm exam
9	Parametric representation of a curve in space, velocity vector, covariant derivative
10	Frenet vectors of a curve, Frenet planes
11	Curves, geometrical interpretation of the curves
12	The circle of curvature, curvature sphere, the axis of curvature
13	Osculator sphere. Spherical curves. Inclined curves
14	Involute and evolute. Bertrand curve pairs
15	Bertrand curve pairs
16	Global indicators of a curve

Recommended or Required Reading

1 H. Hilmi Hacısalihoğlu,Differential Geometry, İnönü Üniversitesi, 1983. 2 Barret O’Neill, Elementary Differential Geometry, Academıc Pres Inc. 1966 3 Arif Sabuncuoğlu, Diferensiyel Geometri, Nobel yayınları, 2001.

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
SUM		0
End Of Term (or Year) Learning Activities	Quantity	Weight
SUM		0
Yarıyıl (Yıl) İçi Etkinlikleri		40
Yarıyıl (Yıl) Sonu Etkinlikleri		60
SUM		100

Language of Instruction

Turkish

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	2	2
Final Examination	1	2	2
Makeup Examination	1	2	2
Attending Lectures	14	4	56
Problem Solving	10	4	40
Self Study	10	2	20
Individual Study for Mid term Examination	6	5	30
Individual Study for Final Examination	4	5	20
TOTAL WORKLOAD (hours)			172

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7
LO1	3	3	4	5	4	5	5

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High